math192_hw10sp06

# math192_hw10sp06 - HW10 Solutions 16.1 Line Integrals 1....

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HW10 Solutions 16.1 Line Integrals 1. (c) 2. (e) 3. (g) 4. (a) 5. (d) 6. (b) 7. (f) 8. (h) 10. r ( t ) = t i + (1 t ) j + k , t 1 d r dt = i j | d r dt | = 2; x = t, y = 1 t, z = 1 x y + z = 2 = t (1 t ) + 1 2 = 2 t 2 integraltext c f ( x,y,z ) ds = integraltext 1 (2 t 2) 2 dt = 2[ t 2 2 t ] 1 = 2 12. r ( t ) = (4 cos t ) i + (4 sin t ) j + 3 t k , 2 t 2 d r dt = ( 4 sin t ) i + (4 cos t ) j + 3 k | d r dt | = radicalbig 16 sin 2 t + 16 cos 2 t + 9 = 5 radicalbig x 2 + y 2 = radicalbig 16 cos 2 t + 16 sin 2 t = 4 integraltext c f ( x,y,z ) ds = integraltext 2 - 2 (4)(5) dt = [20 t ] 2 - 2 = 80 16. integraltext C f ( x,y,z ) ds = integraltext C 1 fds + integraltext C 2 fds + integraltext C 3 fds = 1 3 + ( 1 3 ) = 1 2 = 1 6 20. r ( t ) = (1 t ) i + 1 2 (1 t ) 2 j , t 1 | d r dt | = radicalbig 1 + (1 t ) 2 ; f ( x,y ) = f ( (1 t ) , 1 2 (1 t ) 2 ) = (1- t )+ 1 4 (1- t ) 4 1+(1- t ) 2 integraltext C fds = integraltext 1 (1- t )+ 1 4 (1- t ) 4 1+(1- t ) 2 radicalbig 1 + (1 t ) 2 dt = integraltext 1 ( (1 t ) + 1 4 (1 t ) 4 ) dt = bracketleftbig 1 2 (1 t ) 2 1 20 (1 t ) 5 bracketrightbig 1 = 0 ( 1 2 1 20 ) = 11 20 24. r ( t...
View Full Document

## This note was uploaded on 02/05/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

### Page1 / 3

math192_hw10sp06 - HW10 Solutions 16.1 Line Integrals 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online